Influence of layer separation and doping on plasmons of double-layer α-T₃ lattices

We have investigated the spectrum of alpha-T3 plasmons which arise when a pair of lattice sheets have a finite separation between them with a dielectric medium between them. The procedure we used is a calculation of the surface response function which is calculated by matching the electrostatic potential across an interface as well as relating the discontinuous electric field at each interface to its charge density on the conducting layer. Using the linear response theory, we introduce the polarization function. We determine the plasma excitations for various layer separations, dielectric media between and surrounding the layers, and doping concentrations.